The December figure was revised up from 6.5% previously estimated.
In January 2012, the jobless rate was 7.4%.
An estimated 660,000 people were unemployed and looking for work in January, down from 671,000 a month earlier. Male jobless rate was 6.9%, while female unemployment reached 6.2%.
The figures refer to people aged between 15 and 74 and are based on the definition recommended by the International Labor Organization.
The unemployment rate for people aged 25-74 was 5.2% in January, the data showed. The latter category made up for 72.3% of the total jobless people in the first month of 2013.